ICTP-EAIFR  is pleased to invite you to the first ever thesis defense of one of our PhD students: Mr. Tony Kakona.

• Speaker: Mr  Tony Mbambu Kakona (ICTP-EAIFR)
• Date: Tuesday 6 December, 2022
• Time: 10:00 – 11:30 HRS (GMT+2)
• Venue: ICTP and Online
• Title: Topological Gauge Theories with Non-Compact Groups

Mr Tony Kakona will give a presentation based on his thesis for about 45 minutes, which will be followed by questions from the PhD examiners and others.

 Abstract: Topological Gauge theories offer an arena where one may have non-compact gauge groups without the issues of unitarity and renormalisability. However, Topological Gauge Theories do have their own problems that one must contend with. The path integrals usually become finite integrals over moduli spaces and singularities in the moduli spaces that arise or non-compactness are manifested in the the presence of zero modes in the field theory which must be dealt with in some form or another.

For this thesis, I consider two types of topological gauge theories with non compact gauge groups. The first, has essentially Abelian non-compact gauge group and represents the Ray-Singer Torsion in any dimension, while the second, with non-Abelian gauge group, is a variant of the well known Chern-Simons theory, namely the so-called BF theory on 3-dimensional manifolds. There are, just as described in the general case, issues in the evaluation of the partition functions in these theories due to zero-modes.

The first part of the thesis is devoted to the analytic Ray-Singer Torsion in any dimension. These theories have a non-compact shift type gauge symmetry. Being a key ingredient in the evaluation of the BF partition function, I address the issues of zero modes related to such an object and introduce a new type of regularisation of the Ray-Singer Torsion (whose definition consists of a product of determinants of twisted Laplacians) by the addition of a mass. As a result, one is able to follow the singular behaviour and extract meaningful quantities. A number of general properties of this massive Ray-Singer Torsion are given. For mapping tori and related product manifolds one is able to interpret the mass term as a flat R+ connection and one can represent the massive Ray-Singer Torsion as the path integral of a Schwarz type topological gauge theory.

The second and last part of this thesis focuses on BF theories in 3-dimensions. The non-compact symmetry of the Ray-Singer Torsion theories of the first part now combine with the compact gauge group G to give a TG gauge invariance for the BF theory. I concentrate on the evaluation of the BF theory path integral partition function in the cases of Integral and Rational Homology 3-Spheres. With the aid of the Abelianisation technique, the end result is a finite integral over the tangent space to the Cartan subalgebra of the compact group G. However these finite dimensional integrals are singular with a number of poles on the integration contour. The point here is an attempt to give a meaning to the partition function from first principles. I propose three different definitions of the 3-dimensional BF partition function and discuss their advantages as well as their limitations.

Short bio: Mr Tony Mbambu Kakona originally from the Democratic Republic of Congo (DRC) obtained a bachelor's degree in Physics from the University of Kinshasa (DRC) and 2 postgraduate diplomas, one in (applied)  Nuclear Physics (CRNA, Algeria) and the other in Theoretical Physics (ICTP, Italy). He is currently a PhD student at ICTP-EAIFR, working on topological field theories under the supervision of Prof George Thompson (ICTP).

Zoom Meeting ID: 942 0886 7189; Password: 080808

Link: https://zoom.us/j/94208867189